The invention relates to a method of generating a control program, according to which a laser-beam spot is guided, while being controlled with respect to position and time, over a cornea to be corrected, so as to ablate a predetermined ablation profile therefrom. The invention also relates to an electronic computer and to a device for corneal surgery of the eye, in which a control program generated by means of the method is used.
Photorefractive keratectomy has become a widely established method of correcting lower-order visual disorder, for example myopia, hyperopia, astigmatism, myopic astigmatism and hyperopic astigmatism. The term “photorefractive keratectomy (PRK)” is usually understood as meaning only intervention on the corneal surface, after the so-called corneal epithelium has been removed. After the epithelium is removed, the Bowman's membrane, or corneal stroma, is exposed and can be ablated using a laser. Distinction is generally made between PRK and the LASIK method (Laser In Situ Keratomileusis). In the LASIK method, a so-called microkeratome is firstly used to excise an approximately 100 μm to 200 μm-thick corneal flap with a diameter of from 8 to 10 mm, leaving only a small remnant which acts as a “hinge”. This flap is folded to the side, and then material is ablated (removed) by means of laser radiation directly in the stroma, i.e. not at the corneal surface. After the laser treatment, the cover is folded back to its original place, and relatively fast healing generally takes place.
The invention described below is suitable both for the aforementioned PRK and, in particular, for the LASIK technique.
In PRK and in LASIK, material of the cornea is ablated. The ablation is a function of the laser beam's energy density (energy per unit area) incident on the cornea. Various techniques for shaping the beam and guiding the beam are known, for example so-called slit scanning, in which the radiation is guided, by means of a moving-slit, over the area to be processed, so-called spot scanning, in which a radiation spot of very small dimensions is guided over the region to be ablated, and so-called full ablation, or wide-field ablation, in which the radiation is projected with a wide field over the full area to be ablated, and where the energy density changes across the beam profile in order to achieve the desired ablation of the cornea. For the said forms of beam guidance, the prior art contains respectively suitable algorithms for controlling the radiation, in order to ablate the cornea in such a way that the desired radius of curvature is finally imparted to the cornea.
The “spot scanning” already mentioned above uses a laser beam which is focused onto a relatively small diameter (0.1-2 mm), which is directed at various positions on the cornea by means of a beam-guiding instrument and which is successively moved, by a so-called scanner, so that the desired ablation from the cornea is finally achieved. The ablation hence takes place according to a so-called ablation profile. In particular, so-called galvanometric scanners can be used in PRK and LASIK (cf. the article by G. F. Marshall in LASER FOCUS WORLD, June 1994, p. 57). Since then, other scan techniques have been disclosed for guiding the laser beam.
According to the prior art, the said lower-order visual disorders (e.g. myopia, hyperopia, astigmatism) are currently performed [sic] according to the so-called refraction data of the patient's eye, i.e. the dioptric value measured for the patient's eye dictates the ablation profile according to which material will be removed (ablated) from the cornea (cf. T. Seiler and J. Wollensak in LASERS AND LIGHT IN OPHTHALMOLOGY, Vol. 5, No 4, pp. 199-203, 1993). According to this prior art, for a given patient's eye with a particular dioptric value, the laser radiation is hence guided over the cornea in such a way that a predetermined ablation profile is removed, for example according to a parabola when correcting myopia. In other words: the ablation profile is matched to the individual eye only according to the dioptric value, but not according to local non-uniformities of the “eye” optical system.
The article by J. K. Shimmick, W. B. Telfair et al. in JOURNAL OF REFRACTIVE SURGERY, Vol. 13, May/June 1997, pp. 235-245, also describes the correction of lower-order sight defects by means of photorefractive keratectomy, where the photoablation profiles correspond to theoretical parabolic shapes. Furthermore, this citation only proposes that a few empirical correction factors, which take account of the interaction between the laser and the tissue, be added in to the ablation profile in order thereby to achieve paraboloidal ablation on the eye.
A particular problem in photorefractive keratectomy and LASIK involves the relative positioning of the laser beam and the eye. The prior art contains various methods for this, for example so-called eye-trackers, i.e. instruments which determine the eye's movements so that the laser beam used for the ablation can then be controlled (tracked) in accordance with the ocular movements. The prior art relating to this is described, for example, by DE 197 02 335 C1.
As mentioned above, the methods of photorefractive corneal surgery in the prior art for correcting lower-order visual disorder are essentially “wholesale” methods, in so far as the correction is based on the (wholesale) dioptric value of the eye. Such lower-order visual disorder can be corrected, for example, by spherical or astigmatic lenses, or indeed by photorefractive correction of the cornea.
However, the optical imaging in the eye is impaired not only by the said lower-order visual disorders, but also by so-called higher-order image defects. Such higher-order image defects occur, in particular, after operative interventions on the cornea and inside the eye (cataract operations). Such optical aberrations can be the reason why, despite medical correction of a lower-order defect, full visual acuity (sight) is not achieved. P. Mierdel, H.-E. Krink, W. Wigand, M. Kaemmerer and T. Seiler describe, in DER OPHTALMOLOGE [THE OPHTHALMOLOGIST], No 6, 1997, p. 441, a measuring arrangement for identifying the aberration of the human eye. With such a measuring arrangement, it is possible to measure aberrations (imaging defects) for monochromatic light, and moreover not only aberrations due to the cornea, but also the imaging defects caused by the entire ocular imaging system of the eye can be measured, and actually as a function of position, i.e. with a particular resolution it is possible to determine, for given locations inside the pupil of the eye, how great is the imaging defect of the entire optical system of the eye to be corrected, at this position. Such imaging defects of the eye are mathematically described as a so-called wavefront aberration in the work by P. Mierdel et al. cited above. The term “wavefront aberration” is used to mean the spatial variation of the distance between the actual light wavefront from a central light point and a reference surface, e.g. its ideal spherical configuration. For instance, the sphere surface of the ideal wavefront is used as the spatial reference system. As the reference system for measuring the aberration, a plane is chosen when the ideal wavefront to be measured is plane.
The measuring principle according to the said work by P. Mierdel, T. Seiler et al. is also used in PCT/EP00/00827. It essentially involves splitting a parallel beam bundle of sufficient diameter through a hole mask into separate parallel individual beams. These individual beams pass through a converging lens (the so-called aberroscope lens) so that they are focused at a particular distance in front of the retina in the case of an emmetropic eye. The result is highly visible projections of the mask holes on the retina. This retinal light-point pattern is imaged, according to the principle of indirect ophthalmoscopy, onto the sensor surface of a CCD video camera. In the aberration-free ideal eye, the imaged-light-point pattern is undistorted and corresponds exactly to the hole-mask pattern. If there is an aberration, however, then individual displacements of each pattern point occur, because each individual beam passes through a particular corneal or pupillary area and experiences a deviation from the ideal path according to the non-uniform optical effect. From the retinal pattern-point displacements, the wavefront aberration is finally determined by an approximation method as a function of position over the pupillary surface. The said prior art also describes the mathematical representation of this wavefront aberration in the form of a so-called “wavefront-aberration hill”. Above each pupillary location (x-y coordinates), this “wavefront-aberration hill” indicates a value of the wavefront aberration W(x,y) which is then plotted as a height above the x-y coordinates. The higher the “hill” is, the greater are the imaging consumptions [sic] in the eye at the respective pupillary location. For each incident light beam, there is to first approximation a proportionality between the measured deviation of the corresponding retinal light point from its ideal position and the gradient of the “wavefront-aberration hill”. The wavefront aberration can hence be identified from this as a function of position, with respect to an arbitrary reference value on the optical axis of the system. Ideal, in general undistorted light-point positions on the retina, which can yield the reference value, are for example four central points at a small distance from one another. Such points represent a central corneal/pupillary zone of about 1 to 2 mm in diameter, which from experience can be assumed to be substantially free of higher-order image defects.
The “wavefront-aberration hill” can be mathematically represented in various ways with the use of a closed expression (a function). Suitable examples include approximations in the form of a sum of Taylor polynomials or, in particular, Zernike polynomials. The Zernike polynomials have the advantage that their coefficients have a direct relationship with the well known image defects (aperture defects, coma, astigmatism, distortion). The Zernike polynomials are a set of completely orthogonal functions. An article by J. Liang, B. Grimm, S. Goelz and J. F. Bille, “Objective Measurement of Wave Aberrations of the Human Eye with the use of a Hartmann-Shack Wavefront Sensor”, Optical Society of America, 11(7): 1949-1957, July 1994, shows how the wavefront (or wavefront aberration) can be calculated from the grid-point displacements. From identifying the derivative function of the wavefront, it is hence possible to determine the actual wavefront. The wavefront is found as the solution of a system of equations. The article by H. C. Howland and B. Howland, “A Subjective Method for the Measurement of Monochromatic Aberrations of the Eye”, Journal of the Optical Society of America 67(11): 1508-1518, November 1977, also describes a method for identifying monochromatic aberration and the determination of the first fifteen Taylor coefficients.
The device proposed in the aforementioned PCT/EP00/00827 for photorefractive corneal surgery in the case of higher-order sight defects has the following instruments:                an aberroscope for measuring the wavefront aberration of the entire optical system of the eye to be corrected, with respect to a particular ocular position,        means for deriving a photoablation profile from the measured wavefront aberration so that photoablation according to the photoablation profile minimises the wavefront aberration of the eye being treated, and        a laser-radiation source and means for controlling the laser radiation with respect to the particular ocular position, in order to ablate the photoablation profile.        
And, if this device produced significant improvements compared with the previous solutions, it was found that the treatment successes in some cases were not as good as might have been expected in view of the accuracy with which the photoablation profile had been compiled.
It is therefore an object of the present invention to provide a way in which even better treatment successes can be achieved.
The invention is based on the discovery that in the prior art, although a very accurate ablation profile was determined, the simplifying assumption was nevertheless made, when carrying out the ablation, that the laser beam induces uniform ablation at each location on the cornea. However, the laser beam is incident with different angles at the various locations on the cornea. This has two consequences: on the one hand, the density of the laser-beam energy incident on the corneal surface changes with this angle and, on the other hand, a differing fraction of the incident laser radiation is reflected depending on the angle.
The invention correspondingly provides a method of generating a control program of the generic type mentioned in the introduction, in which, when generating the control program, the effect of the angle between the laser beam and the corneal surface on the energy density of the laser-beam spot incident on the corneal surface is taken into account.
Alternatively or additionally, account is taken of the fact that a fraction of the laser-beam energy incident on the corneal surface is reflected away.